## Self-interacting random walks and statistical physics [MA5941]

### Summer semester 2020

**Homepage:** at NYU Shanghai ^{}
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#### (Recommended) requirements:

MA2409 probability theory, MA2404 Markov chains

#### Contents:

The aim of the course is to introduce to some generic techniques for the study of self-interacting random walks, and to explain the links that appeared recently with statistical physics, in particular with the supersymmetric hyperbolic sigma model arising in random matrix theory, with a random Schrödinger operator and with the so‐called Dynkin isomorphism and Ray-Knight local time approaches. More information can be found

here.

#### Exam

The exam will be in oral form (30 minutes). Students demonstrate that they have gained deeper knowledge of definitions and main mathematical tools
and results on self-interacting random walks, particularly linearly edge-reinforced random walk, vertex-reinforced jump process, and their link to statistical physics.